Confusion matrix questions

Imagine a spam filter model where emails labeled 1 = spam, 0 = not spam.

If a spam email is incorrectly classified as not spam, what kind of error is this?

• 1. A false positive
• 2. A true positive
• 3. A false negative
• 4. A true negative

Confusion matrix questions

In an intrusion detection system, 1 = intrusion, 0 = safe.

If the system misses an actual intrusion and classifies it as safe, this is a:

• 1. A false positive
• 2. A true positive
• 3. A false negative
• 4. A true negative

Confusion matrix questions

In a medical test for a disease, 1 = diseased, 0 = healthy.

If a healthy patient is incorrectly diagnosed as diseased, that’s a:

• 1. A false positive
• 2. A true positive
• 3. A false negative
• 4. A true negative

Metrics other than accuracy

Now that we understand the different types of errors, we can explore metrics that better capture model performance when accuracy falls short, especially for imbalanced datasets.

We’ll start with three key ones:

• Precision

• Recall

• F1-score

• Precision

• Recall

• F1-score

Precision and recall

Let’s revisit our fraud detection scenario. The circle below represents all transactions predicted as fraud by an imaginary toy model designed to detect fraudulent activity.

Intuition behind the two metrics

• Precision answers:
  > Of all the transactions predicted as fraud, how many were actually fraud?
  High precision \(\rightarrow\) few false alarms (low false positives).

• Recall answers:
  > Of all the actual fraud cases, how many did the model catch?
  High recall \(\rightarrow\) few missed frauds (low false negatives).

Trade-off between precision and recall

• Increasing recall often decreases precision, and vice versa.
  
• Example:
  • Predict “fraud” for every transaction \(rightarrow\) perfect recall, terrible precision.
    
  • Predict “fraud” only when 100% sure \(rightarrow\) high precision, low recall.

The right balance depends on the application and cost of errors.

F1-score

• Sometimes, we want a single metric that balances precision and recall.
  
• The F1-score is the harmonic mean of the two:

\[ F1 = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} \]

• High F1 means both precision and recall are strong.
  
• Useful when we care about both false positives and false negatives.

Summary

iClicker Exercise 9.1

Select all of the following statements which are TRUE.

• 1. In medical diagnosis, false positives are more damaging than false negatives (assume “positive” means the person has a disease, “negative” means they don’t).
• 2. In spam classification, false positives are more damaging than false negatives (assume “positive” means the email is spam, “negative” means they it’s not).
• 3. If method A gets a higher accuracy than method B, that means its precision is also higher.
• 4. If method A gets a higher accuracy than method B, that means its recall is also higher.

Counter examples

Method A - higher accuracy but lower precision

Method B - lower accuracy but higher precision

Thresholding

• The above metrics assume a fixed threshold.

• We use thresholding to get the binary prediction.

• A typical threshold is 0.5.

  • A prediction of 0.90 \(\rightarrow\) a high likelihood that the transaction is fraudulent and we predict fraud
  • A prediction of 0.20 \(\rightarrow\) a low likelihood that the transaction is non-fraudulent and we predict Non fraud

• What happens if the predicted score is equal to the chosen threshold?

• Play with classification thresholds

iClicker Exercise 9.2

Select all of the following statements which are TRUE.

• 1. If we increase the classification threshold, both true and false positives are likely to decrease.
• 2. If we increase the classification threshold, both true and false negatives are likely to decrease.
• 3. Lowering the classification threshold generally increases the model’s recall.
     
• 4. Raising the classification threshold can improve the precision of the model if it effectively reduces the number of false positives without significantly affecting true positives.

PR curve

• Calculate precision and recall (TPR) at every possible threshold and graph them.
• Better choice for highly imbalanced datasets

ROC curve

• Calculate the true positive rate (TPR) and false positive rate (FPR) at every possible thresholding and graph TPR over FPR.
• Good choice when the datasets are roughly balanced.

AUC

• The area under the ROC curve (AUC) represents the probability that the model, if given a randomly chosen positive and negative example, will rank the positive higher than the negative.

ROC AUC questions

Consider the points A, B, and C in the following diagram, each representing a threshold. Which threshold would you pick in each scenario?

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